Question

find the volume of this object. use 3 for π. volume of a cylinder v = πr²h volume of a cone v = \frac{πr²h}{3} first lets calculate the volume of the cylinder. v = π?² hint: plug in the value of the radius. the diameter is 8. the radius is half this value.

Explanation:

Step1: Calculate radius of cylinder and cone

The diameter is 8 cm, so the radius $r=\frac{8}{2}=4$ cm.

Step2: Calculate volume of cylinder

Using the formula $V_{cylinder}=\pi r^{2}h$, with $\pi = 3$, $r = 4$ cm and $h = 12$ cm.
$V_{cylinder}=3\times4^{2}\times12=3\times16\times12 = 576$ $cm^{3}$.

Step3: Calculate volume of cone

Using the formula $V_{cone}=\frac{1}{3}\pi r^{2}h$, with $\pi = 3$, $r = 4$ cm and $h = 10$ cm.
$V_{cone}=\frac{1}{3}\times3\times4^{2}\times10=1\times16\times10 = 160$ $cm^{3}$.

Step4: Calculate total volume of the object

$V = V_{cylinder}+V_{cone}=576 + 160=736$ $cm^{3}$.

Answer:

$736$ $cm^{3}$